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Markowsky, George

The representation of posets and lattices by sets. (English) Zbl 0449.06007

Algebra Univers. 11, 173-192 (1980).
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Cited in 13 Documents

MSC:

06B15 Representation theory of lattices
06B23 Complete lattices, completions
06A06 Partial orders, general
06D05 Structure and representation theory of distributive lattices
05A15 Exact enumeration problems, generating functions

Keywords:

number of sup-preserving representations of a finite lattice; finite distributive lattices; number of order-isomorphic representations; complete lattices
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Full Text: DOI

References:

[1] Birkhoff, G.,Lattice Theory, A. M. S. Colloquium Publ., Vol.25, 3rd., Providence, 1967.
[2] Birkhoff, G. andO. Frink,Representations of Lattices by Sets, Trans. AMS64 (1948), 299–316. · Zbl 0032.00504 · doi:10.1090/S0002-9947-1948-0027263-2
[3] Blyth, T. S. andM. F. Janowitz,Residuation Theory, Pergamon Press, Oxford, 1972.
[4] Brandon, R. L., K. K.-H. Butler, D. W. Hardy andG. Markowsky,Cardinalities of D-Classes in B n, Semigroup Forum 4 (1972), 341–344. · Zbl 0253.05006 · doi:10.1007/BF02570807
[5] Brandon, R. L., D. W. Hardy andG. Markowsky,The Schutzenberger Group of an H-class in the Semigroup of Binary Relations, Semigroup Forum5 (1972), 45–53. · Zbl 0259.20056 · doi:10.1007/BF02572873
[6] Crawley, P. andR. P. Dilworth,Algebraic Theory of Lattices, Prentice-Hall, Englewood Cliffs, N. J., 1973. · Zbl 0494.06001
[7] Croisot, R.,Applications Residuees, Ann. Sci. Ecole Norm. Sup., Paris (3),73 (1956), 453–474. · Zbl 0073.01103
[8] Derderian, J. C.,Residuated Mappings, Ph. D. Thesis, Wayne State University, 1965.
[9] Dilworth, R. P.,Lattices with Unique Irreducible Decompositions, Annals of Math.41 (1940), 771–777. · Zbl 0025.10202 · doi:10.2307/1968857
[10] Foulis, D. J.,Orthomodular Lattices, mimeographed lecture notes, University of Florida, 1964.
[11] Greene, C. andG. Markowsky,A Combinatorial Test for Local Distributivity, Research Report RC5129, IBM T. J. Watson Research Center, Yorktown Heights, New York, 1974.
[12] Hillman, A.,On the number of Realizations of a Hasse Diagram by Finite Sets, Proc. AMS6 (1955), 542–8. · Zbl 0066.26304 · doi:10.1090/S0002-9939-1955-0074380-6
[13] Liu, C. L.,Introduction to Combinatorial Mathematics, McGraw-Hill, N. Y., 1968. · Zbl 0188.03801
[14] MacLane, S.,Categories for the Working Mathematician, Springer-Verlag, New York, 1971. · Zbl 0705.18001
[15] Markowsky, G.,Combinatorial Aspects of Lattice Theory with Applications to the Enumeration of Free Distributive Lattices, Ph. D. Thesis, Harvard Univeristy, 1973. · Zbl 0302.06010
[16] Markowsky, G.,The Factorization and Representation of Lattices, Trans. AMS 203 (1975), 185–200. · Zbl 0302.06011 · doi:10.1090/S0002-9947-1975-0360386-3
[17] Markowsky, G.,Some Combinatorial Aspects of Lattice Theory, Proc. Univ. of Houston Lattice Theory Conf., Houston 1973, 36–68. · Zbl 0302.06010
[18] Markowsky, G.,Idempotents and Product Representations with Applications to the Semigroup of Binary Relations, Semigroup Forum5 (1972), 95–119. · Zbl 0264.20047 · doi:10.1007/BF02572880
[19] Nau, D. S., G. Markowsky, M. A. Woodbury andD. B. Amos,A Mathematical Analysis of Human Leukocyte Antigen Serology, Math. Biosciences40, 1978, 243–270. · Zbl 0394.92007 · doi:10.1016/0025-5564(78)90088-3
[20] Ore, O.,Galois Connections, Trans. AMS,55 (1944), 494–513.
[21] Riviere, N. M.,Recursive Formulas on Free Distributive Lattices, J. Combinatorial Theory5, 229–234. · Zbl 0243.06005
[22] Whitehead, J. H. C.,Duality Between CW-Lattices, Symp. Internacional de Topologic Algebraic, Mexico (1958), 248–258. Also found inThe Mathematical Works of J.H.C. Whitehead, Ed. by I. M. James, Pergamon Press, London (1962), Vol.4, 179–189.
[23] Zaretskii, K. A.,The Representations of Lattices by Sets, Uspekhi Mat. Nauk (Russian)16 (1961) 153–154.
[24] Zaretskii, K. A.,The Semigroup of Binary Relations, Mat. Sbornik, (Russian)61 (1963), 291–305.
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